Replaced the filter in my KitchenAid fridge with a new one - specifically, "EveryDrop by Whirlpool Refrigerator Water Filter 4 (Pack of 2)" from Amazon. It worked for a day or two, and then the water stopped flowing, accompanied by a very loud, annoying, disturbing jackhammer sound. In addition, upon removing the filter, the refrigerator's filter head (i.e. the "nipple") would leak water non-stop until either a filter or bypass plug were inserted, creating a big mess.
I called a repairman. He inserted a bypass plug, and the water ran fine. Because the bypass cap was long ago lost or thrown away by someone, I could not test this myself. He concluded that both of the filters I bought were defective, charged me $120, and went on his way. This smelled bad, but I had no information with which to counter the decision.
My partial solution
At the suggestion of someone here, I put the filter in a bucket and filled it entirely with water, forcing out all the air within. The effect has been threefold: first, the jackhammer noise can now only be heard for a couple seconds, then it goes away; second, the water now runs, albeit very slowly; third, when removing the filter, the filter head no longer leaks water. I'm very grateful for the latter, because now troubleshooting is less messy.
So, I've decided to live with the crappy water pressure and brief jackhammer sound. Between the overpriced OEM filters, the "repair" job, and a replacement bypass plug, I am about $220 in the hole. I'll wait until the filters give out before trying to contend with this problem again.
This issue is all over the Web, and I do think the most common cause is a bad product. Simply replacing the filter shouldn't break anything, but it does. I don't have a technical explanation for the issue, but it could not have been a coincidental, simultaneous failure of the refrigerator, or my home's water system. It must be a problem with come kind of interaction between the fridge and the filter.